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Construction and Use of the Frequency-Energy Plot for a System With Two Essential Nonlinearities

[+] Author Affiliations
Sean A. Hubbard, Alexander F. Vakakis, Lawrence A. Bergman, D. Michael McFarland

University of Illinois at Urbana-Champaign, Urbana, IL

Paper No. DETC2011-48576, pp. 449-456; 8 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5478-5
  • Copyright © 2011 by ASME


We consider the problem of depicting possible periodic motions of a strongly nonlinear system in the frequency-energy plane. The particular case of a 2-degree-of-freedom, linear primary structure coupled to a 2-DOF, nonlinear attachment is examined in detail. While there exist numerical tools for the semiautomatic computation of such frequency-energy plots (FEPs), the presence of multiple essential (nonlinearizable) nonlinearities in the present system introduces new challenges in their application. Furthermore, the multiple degrees of freedom of the nonlinear subsystem allow the existence of complex nonlinear normal modes localized there but exhibiting more complicated resonances than those previously observed in the study of a single-DOF nonlinear attachment. The FEP generated for a laboratory-scale mechanical system is interpreted to explain the transitions and energy transfers that occur in the simulated transient response of the combined system following broadband shock excitation.

Copyright © 2011 by ASME



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